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The continuous annealing process line (CAPL) of cold rolling is an important unit to improve the mechanical properties of steel strips in steel making. In continuous annealing processes, strip tension is an important factor, which indicates whether the line operates steadily. Abnormal tension profile distribution along the production line can lead to strip break and roll slippage. Therefore, it is essential to estimate the whole tension profile in order to prevent the occurrence of faults. However, in real annealing processes, only a limited number of strip tension sensors are installed along the machine direction. Since the effects of strip temperature, gas flow, bearing friction, strip inertia, and roll eccentricity can lead to nonlinear tension dynamics, it is difficult to apply the first-principles induced model to estimate the tension profile distribution. In this paper, a novel data-based hybrid tension estimation and fault diagnosis method is proposed to estimate the unmeasured tension between two neighboring rolls. The main model is established by an observer-based method using a limited number of measured tensions, speeds, and currents of each roll, where the tension error compensation model is designed by applying neural networks principal component regression. The corresponding tension fault diagnosis method is designed using the estimated tensions. Finally, the proposed tension estimation and fault diagnosis method was applied to a real CAPL in a steel-making company, demonstrating the effectiveness of the proposed method.